A Refined Theory of Elastic‐Plastic Shells at Moderate Rotations

Schmidt, Rüdiger; Weichert, Dieter

doi:10.1002/zamm.19890690106

Cited by 30 publications

(15 citation statements)

References 41 publications

(6 reference statements)

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“…Donnell [26] and Koiter [18,19], numerous works have been devoted to establish linear and non linear elastic shell model using direct or surfacic approaches [5,6,17,34], and even elasto-plastic or plastic shell models [1,32,33]. More recently, the asymptotic methods have been used, to try to justify rigorously from the three-dimensional equations the shell models obtained by direct approaches relying on a priori assumption, and to construct new models [15,16].…”

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confidence: 99%

Computing singular perturbations for linear elliptic shells

2007

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This paper is devoted to the theoretical and numerical study of singular perturbation problems for elliptic inhibited shells. We present a reduction of the classical membrane equations to a partial differential equation with respect to the bending displacement, which is well adapted to the study of singularities of the limit problem. For a discontinuous loading or when the boundary of the loading domain presents corners, we put in a prominent position the existence of two kinds of singularities. One of them is not classical; it reduces to a logarithmic point singularity at the corner of the loading domain. To finish numerical simulations are performed with a finite element software coupled with an anisotropic adaptive mesh generator. They enable to visualize precisely the singularities predicted by the theory with only a very small number of elements.

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confidence: 99%

Computing singular perturbations for linear elliptic shells

2007

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“…Here, a layered shell model incorporating first-order shear deformation theory as well as physical and geometrial nonlinearities was employed. [5] Section 4: Structural Mechanics…”

Section: Experimental Observationsmentioning

confidence: 99%

Limit States in Alternately Loaded Plates

Todres

Stoffel

Weichert

2010

Proc Appl Math and Mech

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In the present study, a circular plate is inelastically deformed by uniform pressure, which is released and then alternately applied to the same peak level. For each iteration, snap-through occurs at an increased pressure relative to the previous one, leading to additional inelastic deformation. At some point, either the plate fails or a limit state of deformation is reached under peak pressure without snap-through. This phenomenon is studied experimentally and theoretically to determine the conditions under which the limit state is stable.

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“…For the structural modeling and numerical simulation a geometrical nonlinear first-order shear deformation shell theory is used, assuming small strains and moderate rotations. The derivation of this shell theory can be found in [4]. In order to trace the evolution of the inelastic material properties in different points in the shell space seperately, the shell is divided into layers.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Validation of constitutive laws for simulations of the dynamic response of plates

Stoffel

Schmidt

Weichert

2003

Proc Appl Math and Mech

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If strain rate dependent deformations of metal plates are studied, it is necessary to use viscoplastic laws for the simulations of the structural response. For this purpose an efficient viscoplastic model is searched in this study. Theoretical frameworkIn order to calculate deformations of shock wave loaded plates the viscoplastic models of Lemaitre-Chaboche [3], Tanimura [6] and Bodner-Partom [1] are applied assuming perfectly plastic material behaviour. As long as the constitutive equations of Chaboche and Tanimura are used the elastic part of material behaviour is covered by Hooke's law while the Bodner-Partom law does not seperate between elastic and plastic material properties. The Lemaitre-Chaboche model is expressed by the following equations:Here, ε p ij , σ ij , k, J 2 (), σ v denote the plastic strain tensor, the stress tensor, the yield limit, the second invariant and the overstress, respectively. The material parameters v, K must be identified from uniaxial tension test. The Tanimura model is presented as followṡwith the material parameters S 0 , r, τ * and the Bodner-Partom model is expressed bẏwith the material paramters are R 0 , D 0 , n. In order to identify the material parameters uniaxial tension tests at different strain rates are used. The identification procedure is described in [5]. For the structural modeling and numerical simulation a geometrical nonlinear first-order shear deformation shell theory is used, assuming small strains and moderate rotations. The derivation of this shell theory can be found in [4]. In order to trace the evolution of the inelastic material properties in different points in the shell space seperately, the shell is divided into layers. Details of the numerical approximation are presented in [2]. Experimental set-upFor the exerimental study two different shock tubes are used. In Fig. 1 the principle of a shock tube is shown. The tube consists of a high pressure chamber (HPC) and a low pressure chamber (LPC) seperated by a membrane. The HPC is filled with gas until the membrane bursts. Then, a shock wave travels into the LPC, impinging on the plate specimen and causing viscoplastic vibrations. The middle point displacement of the specimen is measured by a capacitor and the pressure acting on the plate is measured by pressure devices with piezoelectric elements located in a seperate ring flange next to the plate. Both quantitites, pressure and displacement, are measured during the impuls duration. Aluminium plates with 500mm diameter are used in the large shock tube, copper and steel plates with 138mm diameter are examined in the small shock tube. All plates are 2mm thick.

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A Refined Theory of Elastic‐Plastic Shells at Moderate Rotations

Cited by 30 publications

References 41 publications

Computing singular perturbations for linear elliptic shells

Computing singular perturbations for linear elliptic shells

Limit States in Alternately Loaded Plates

Validation of constitutive laws for simulations of the dynamic response of plates

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